The invention relates to a circuit for providing a constant current.
The invention also relates to a method of providing a constant current.
Such circuits are known for the generation of a constant current, independently of variations of temperature, supply voltage, etc. They are mainly used in analog circuits for providing a reference signal for the measurement of analog signals, for example in analog-digital converters or digital-analog converters, or for generating a constant supply current for, for example, sensors. Nowadays constant current references are derived from voltage reference circuits, so-called bandgap reference circuits. The conversion of a voltage to a current depends on the accuracy of a resistor or of the combination of a capacitor and a timer circuit for charging the capacitor by means of the voltage reference and discharging it so as to generate the output current. The components which are generally used for converting a reference voltage into a reference current, i.e. resistors and capacitors, have values which are usually temperature-dependent. In addition, the accuracy of a bandgap reference circuit depends on the compensation of temperature-dependent parameters of the circuit by means of other temperature-dependent parameters. Normally, this compensation is accurate only in a limited temperature range.
It is an object of the invention to provide a circuit for supplying a constant current which does not suffer the disadvantages outlined above.
The circuit according to the invention is for this purpose characterized by means for generating a first and a second of two substantially identical currents, means for supplying a differential current which is the difference between said two substantially identical currents to a first capacitor, means for supplying a variable charging current to at least one second capacitor, means for periodically discharging and subsequently charging again the first and the at least one second capacitor, means for generating a clock signal between two periodic discharges, which clock signal is a measure for the difference in voltage across the first and the at least one second capacitor, means for generating a setting signal for setting both the variable charging current and at least one of the two substantially identical currents in dependence of said clock signal, and means for controlling an element connected as a constant current source with a same signal as the setting signal.
The invention is based on the following recognition. An electric current is formed by a flow of electrons (or holes, which will also be referred to as electrons hereinafter). An electron has a charge q. The charge Q1 transported by a current I1 during a time t is equal to
Q1=I1t=qN1, 
in which N1 is the number of transported electrons. If the transport mechanism determining I1 is controlled by the mutual independent emission of electrons in a device across an energy barrier higher than a few times kB"THgr" (in which kB is the Boltzmann constant and "THgr" is the absolute temperature), N1 will have a Poisson distribution with the standard deviation N1. The Poisson distribution may be approximated for high values of N1 by a standard distribution with an expected value N1 and a standard deviation N1. The standard deviation of Q1 may be written as
"sgr"Q1=qN1=qQ1=qI1t 
A current to which this type of statistic is applicable is said to have xe2x80x9cshot noisexe2x80x9d. Such a current is the saturated drain current of a MOS transistor which is set for the sub-threshold region, i.e. below the threshold voltage.
The difference xcex94I1=I1,axe2x88x92I1,b between two currents I1,a and I1,b having equal expected values I1 but uncorrelated shot noise values, for example such as generated by two MOS transistors set in the same manner, will lead to a fluctuation xcex94Q1=Q1,axe2x88x92Q1,b. For N1=(I1t/q) greater than  greater than 1 this fluctuation by approximation has a standard distribution with an expected value zero and a standard deviation
"sgr"xcex94Q1=(2)"sgr"Q1=2qI1t 
Said xcex94I1 is supplied to an originally discharged capacitor with capacitance C1. A fluctuating voltage U1 then arises across the capacitor with capacitance C1, which voltage by approximation has a standard distribution with an expected value zero and a standard deviation
"sgr"U1=(2qI1t)/C1 
In addition to the capacitor with capacitance C1 mentioned above, there is also an originally discharged capacitor with capacitance C2. The capacitor with capacitance C2 is charged by a current I2. The voltage U2 across this capacitor at moment t will be equal to
U2=(I2t)/C2 
Provided the unequality I2t greater than  greater than q is complied with, the shot noise of I2 can be disregarded. Assuming that a standard distribution holds for U1, the probability that U1 lies in the region (xe2x88x92U2, U2) is given by
P[xe2x88x92U2 less than U1 less than U2]=erf((U2)/((2)"sgr"U1)) 
The function erf (error function) is defined as
erf(x)=(2/(xcfx80))*0∫xexe2x88x92y2dy 
It will be assumed below for simplicity""s sake that the probability P indicated above is equal to 0.5 because this value leads to a simple embodiment of the invention which is yet to be described in more detail. Alternative values of P are also possible and lead to other values of the factor erfxe2x88x921.
The following relation can be derived for the current I2 corresponding to P=0.5 at moment t by means of the relations given above:
I2=(2erfxe2x88x921(0.5))2*(I1/I2)(C2/C1)2(q/t)=0.91*(I1/I2)(C2/C1)2(q/t) 
in which the function erfxe2x88x921 is the inverse of the error function erf.
For a fixed ratio I1/I2 the probability P[xe2x88x92U2 less than U1 less than U2] is a rising function of I2. The probability P can be kept equal to 0.5 on average by sampling the time-dependent voltages U1 and U2 at a given moment T and subsequently increasing I2 if U2 is smaller than the absolute value of U1 or decreasing I2 if U2 is greater than the absolute value of U1. After sampling, the capacitors C1 and C2 are discharged again, time t is reset to zero, and the capacitors C1 and C2 are charged again with the respective currents xcex94I1 and I2, respectively, during a time period T. The resulting current I2 depends exclusively on the time period T, on the ratio of the capacitances C1 and C2, and on the ratio of the currents I1 and I2. The latter two ratios can be kept constant in general, i.e. independent of temperature, supply voltage, etc., with a high degree of accuracy which is given by the mutually attuned properties of the components used. The time period T can be generated with high accuracy by means of a crystal oscillator or an oscillator with a ceramic resonator. The ratios I1/I2 and C2/C1 can be optimized for a fixed value of I2T so as to occupy a minimum circuit surface area of the integrated circuit in the design of an integrated circuit which uses the circuit according to the present invention.
It was assumed in the above that a comparison is made between the absolute value of the voltage U1 across the capacitor having capacitance C1 and the voltage U2 across the capacitor having capacitance C2. The result of this comparison is a signal whereby the current I2 is increased or decreased in steps.
An alternative algorithm consists in that the difference |U1|xe2x88x92U2 is used as a measure for the error in a feedback loop which comprises an integrator which integrates the difference |U1|xe2x88x92U2 continuously, while the capacitors with capacitance values C1 and C2 are periodically discharged in accordance with a given period T. The output of the integrator is then used for controlling the current I2 such that I2 is a continuous and monotonic rising function of the voltage at the output of the integrator.
A feedback loop may be used for keeping the currents I1,a and I1,b equal on average. Provided the feedback loop including said integrator is sufficiently slow, which implies that fluctuations in the error signal are satisfactorily smoothed, the result will be that |U1|xe2x88x92U2 is kept equal to zero on average. Assuming again that a standard distribution is valid for U1, the expected value of |U1|xe2x88x92U2 at moment t is given by
 less than |U1|xe2x88x92U2 greater than =((2/xcfx80))"sgr"U1xe2x88x92U2=(2/C1)((qI1t/xcfx80))xe2x88x92(I2t/C2) 
Starting from this result, the expected value for the error signal averaged over the period T is given by
{overscore ( less than |U1|xe2x88x92U2 greater than )}=(4/(3C1))((qI1T/xcfx80))xe2x88x92(I2T/2C2) 
As was indicated above, the expected value of the average error signal over period T will be equal to zero. Equalizing the preceding equation to zero yields
I2=(64/(9xcfx80))*(I1/I2)(C2/C1)2(q/T) 
This is comparable to the result based on the algorithm in which the current I2 is changed in steps and in which it is exclusively evaluated whether I2 is greater or smaller than |U1|.
It is apparent from the above that it is possible to generate a constant current I2 which is dependent on the ratio of two currents, the ratio of two capacitances, and a fixed time period. Although it is difficult in practice to lay down exactly a given current value and capacitance of a capacitor, it is not difficult in practice to lay down exactly a ratio of two currents and a ratio of two capacitances, especially in the case of integrated circuits. It is also possible to lay down time intervals with high accuracy by means of clock signals derived from a quartz crystal or a ceramic resonator. In particular, a ceramic resonator renders it possible to lay down time intervals with high accuracy. It is particularly notable that the description given above utilizes the extremely small differential current xcex94I1 of two currents I1,a and I1,b which are comparatively strong. Practical embodiments of circuits in which the algorithms described above are used will be explained in more detail below with reference to FIGS. 1 and 2.
The influence of the temperature on the current I2 has been disregarded up to this point, because it was assumed that the initial voltages at the originally discharged capacitors with capacitances C1 and C2 were equal to zero. The following description, like the preceding description, will start from the assumption that the shot noise of I2 can be disregarded, i.e. it is assumed that I2t greater than  greater than q. Any noise in the capacitor with capacitance C2 can be disregarded in that case. It will become apparent below, however, that thermal noise in the discharging of the capacitor with capacitance C1 cannot be disregarded.
It is necessary to short-circuit the capacitor with capacitance C1 by means of a switch, for example a MOS transistor, for discharging this capacitor. Such a switch will always have a finite series resistance R1 which generates thermal noise, i.e. Nyquist noise. Said thermal noise has a spectral density in the noise voltage of 4kB"THgr"R1. After low-pass filtering by the RC network consisting of R1 and C1, this noise causes a fluctuating voltage across C1 with a variance
"sgr"U1,th2=0∫∞(4kB"THgr"R1)/(1+(2xcfx80ƒR1C1)2)dƒ=(kB"THgr")/C1 
in which f is the frequency. The variance is independent of the value of R1. Accordingly, reducing the series resistance of the switch is useless for preventing thermal noise in the originally uncharged capacitors. Reducing the series resistance of the switch does help in speeding up the discharging. After the discharging switch has been opened, a quantity of charge is present in the capacitor with capacitance C1 which is determined by the value of the thermal noise at the moment the switch was opened. This initial thermal noise and the subsequent shot noise are mutually independent. To obtain the variance of the total noise voltage in the capacitor with capacitance C1, the variances of the thermal noise and the shot noise are to be added together:
"sgr"U12=((2qI1t)/C12)+((kB"THgr")/C1)=(q/C1)(((2I1t)/(C1))+((kB"THgr")/q)) 
The xe2x80x9cthermal noisexe2x80x9d kB"THgr"/q at room temperature is approximately 25 mV.
If the first algorithm described above is used, it can be demonstrated that the inclusion of the original thermal noise in the capacitor with capacitance C1 leads to the following corrected result for I2:
I2=2(erfxe2x88x922(0,5))*(I1/I2)*(C2/C1)2*(q/t)*(1+(1+((I2C1)2/(I1C2)2)((C1kB"THgr")/(2erfxe2x88x922(0,5))q2))xc2xd) 
This may be written as
I2=I2,i+I2,d 
in which I2,i is the original temperature-independent result for I2 calculated without taking into account the Nyquist noise, and I2,d is the temperature-dependent portion of I2. In the case of a small correction, i.e. the shot noise dominates over the Nyquist noise, I2,d may be approximated in the first order in "THgr" by
I2,d≈(I2/I1)((C1kB"THgr")/(2qt)) 
It is apparent from the above that I2,i and I2,d are dependent on the ratio I1/I2 and on the capacitances C1 and C2 in different manners. This difference can be utilized for making the temperature-dependent term I2,d small in comparison with the temperature-independent term I2,i through a suitable choice of the components of the circuit.
It is possible on the basis of the above description of the currents I2, I2,i and I2,d to construct a current reference which supplies a current which is independent in the first order of the temperature "THgr". Two current reference circuits, circuit a and circuit b, are designed for this purpose as described above and yet to be described below in more detail with reference to FIGS. 1 and 2. The current reference circuits a and b have different ratios for I2,d/I2,i and the temperature-dependent, constant currents are combined in the following manner:
I0=I2axe2x88x92((I2,da)/(I2,db))I2b 
in which the first-order approximations are used for I2,da and I2,db, which leads to
I2,da/I2,db=(I2a/I2b)(I1b/I1a)(G1a/G1b) 
The current I0 no longer has a linear temperature dependence. Since the first-order approximations of I2,da and I2,db are temperature-dependent, but the quotient of the first-order approximations is temperature-independent, a correction term of the order of "THgr"2 is all that remains for the current I0. If the shot noise dominates over the Nyquist noise, this term with a quadratic temperature dependence can generally be made much smaller than the linear terms in I2a and I2b through a suitable choice of the components.
Following a procedure similar to the one given above in relation to the first algorithm, a temperature-dependent correction term can be found for the current I2 also with the second algorithm. In this case, again, a starting current I0 may be designed which is independent of the temperature in the first order of "THgr".
Alternative combinations of the two currents I2a and I2b may be used for minimizing the temperature dependence, depending on the temperature range.
Algorithms other than the two algorithms described above may be formulated for implementing a balance between a current and the shot noise of this current or of a different current. In addition, more complicated circuits may be designed for eliminating higher-order, for example second-, third-order, etc., temperature-dependent terms in the constant current generated by the circuit.